Question

If alpha and beta are the roots of x square + 5x - 1 = 0 then find
1. Alpha cube + beta cube
2. Alpha square + beta Square

Answer 1

heya
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Alfa³ + Beat³ = ( Alfa + Beta )³ - 3 Alfa × Beta ( Alfa + Beta )


Alfa + Beta = -5


Alfa × Beta = -1



=>


Alfa³ + Beta³ = ( -5)³ -3 ( -1 ) ( -5 )



=>


Alfa ³ + Beta³ = -125- 15


=>


Alfa³ + Beta³ = 140



2)


Alfa² + Beta² = ( Alfa + Beta )² - 2Alfa × Beta


=>


Alfa² + Beta² = 25 +2


=>


Alfa² + Beta² = 27

Answer 2

Heya

_______________________________

ax² + bx + c = 0

Alfa + Beta = -b/a

And

Alfa × Beta = c/a

_______________________________

In given question

Alfa + Beta = -5

And

Alfa × Beta = -1

=>

Alfa³ + Beta³ = ( Alfa + Beta )³ - 3 Alfa × Beta ( Alfa + Beta )

=>

Alfa³ + Beta³ = ( -5 )³ - 3 ( -1 ) ( -5 )

=>

Alfa³ + Beta³ = -125 - 15

=>

Alfa³ + Beta³ = -140

2)

Alfa² + Beta² = ( Alfa + Beta )² - 2 Alfa × Beta

=>

Alfa² + Beta² = 25 + 2

=>

Alfa² + Beta² = 27